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{
"nodes": {
"000": {
"id": "000",
"label": "Logical Statements\nand Operations",
"meta": " SLL01",
"content": "Logic is the foundation to formulate proofs and to understand the language of mathematics.",
"notes": "000-snippet.html",
"video": "https://www.youtube.com/embed/DU4wKBDm2Z4?start=7",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/SDSU/Discrete/Logic/ttcontratautB4.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto000?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"001": {
"id": "001",
"label": "Sets",
"meta": " SLS01 + SLS02 + SLS03 + SLS04 ",
"content": "Sets are the basic building blocks for a lot of mathematics. In order to rigorously define numbers and doing real analysis, we need to know how to work with sets.",
"notes": "001-snippet.html",
"video": "https://www.youtube.com/embed/iA-Dtf7529M?start=14",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Rochester/setSetTheory1/ur_st_1_5.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto001?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/4dhxy6YLYN7ItlWa0QgsG1?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
},
"002": {
"id": "002",
"label": "Real Numbers",
"meta": " SLR03 ",
"content": "In a real analysis, the real numbers are the largest number set we need. They satisfy axioms that represent the idea of a number line.",
"notes": "002-snippet.html",
"video": "https://www.youtube.com/embed/E2MAvASTcg4?start=19",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Mizzou/Intermediate_Algebra/Compound_Inequalities/P_02.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto002?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/1i62R3ZdwhjASp1TNJ2Bcy?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
},
"003": {
"id": "003",
"label": "Maps",
"meta": " SLS04 ",
"content": "Maps are the mathematical formulation of a machine that gets inputs and generate outputs. On both sides, sets are needed.",
"notes": "003-snippet.html",
"video": "https://www.youtube.com/embed/JoLDwNh1lZ8?start=260",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Mizzou/Intermediate_Algebra/Functions_Evaluating/Quad_No_Constant.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto003?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"004": {
"id": "004",
"label": "Natural Numbers\nand Induction",
"meta": " SLN01 + SLN02 + SLN03 + SLN04 ",
"content": "Using natural numbers is our first mathematical abstraction as children. Mathematical induction is an important technique of proof.",
"notes": "004-snippet.html",
"video": "https://www.youtube.com/embed/WMgiYh7tac0?start=13",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/MC/Proofs/EssayProofs/InductionDivisibility01.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto004?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/30dINCx7oSXMkCcSIOIBrv?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
},
"005": {
"id": "005",
"label": "Image and Preimage",
"meta": " SLS05 ",
"content": "Via images and preimages we describe how functions work on sets.",
"notes": "005-snippet.html",
"video": "https://www.youtube.com/embed/twBYYTJdcjc?start=14",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Mizzou/Algebra/functions_domain_range/fun_dom_19.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto005?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"006": {
"id": "006",
"label": "Injectivity, Surjectivity,\nBijectivity",
"meta": " SLS06 ",
"content": "These are important notions for maps.",
"notes": "006-snippet.html",
"video": "https://www.youtube.com/embed/CSzJchEvfpE?start=9",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/UMass-Amherst/Abstract-Algebra/PS-Functions/Functions2.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto006?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"007": {
"id": "007",
"label": "Composition",
"meta": " SLS07 ",
"content": "The composition for maps is just applying two maps in a row.",
"notes": "007-snippet.html",
"video": "https://www.youtube.com/embed/NiJ1yWKM9CU?start=13",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/UMN/algebraKaufmannSchwitters/ks_8_6_18.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto007?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"008": {
"id": "008",
"label": "Logical Deduction",
"meta": " SLL03",
"content": "How to get new true proposition from other true propositions.",
"notes": "008-snippet.html",
"video": "https://www.youtube.com/embed/AjdIPOXRgoQ?start=10",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/ASU-topics/setDiscrete/katie5.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto008?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"009": {
"id": "009",
"label": "Predicates and Quantifiers",
"meta": " SLS01 + SLS02 + SLS03 + SLS04 ",
"content": "Formal mathematical statements are often built by predicates.",
"notes": "009-snippet.html",
"video": "https://www.youtube.com/embed/yIdECC6QExY?start=11",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/SDSU/Discrete/Predicates/predicateB8.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto009?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"010": {
"id": "010",
"label": "Operations on Sets",
"meta": " SLL03",
"content": "Sets can be joined or intersected in order to create new sets.",
"notes": "010-snippet.html",
"video": "https://www.youtube.com/embed/",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/UMN/logicAndSetTheory/prob03.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto010?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"011": {
"id": "011",
"label": "Sums and Products",
"meta": " SLL03",
"content": "An important shorthand notation for calculations.",
"notes": "011-snippet.html",
"video": "https://www.youtube.com/embed/S5DdXfxl3ac?start=3",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Union/setIntSigmaNotation/an6_4_02.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto011?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"012": {
"id": "012",
"label": "Countable Sets",
"meta": "",
"content": "A notion of cardinality that covers finite sets and thos that can be enumerated via the natural numbers.",
"notes": "012-snippet.html",
"video": "https://www.youtube.com/embed/",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Rochester/setSetTheory1/ur_st_1_6.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto012?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/6JdbJSYkihEiLJQijcPkYO?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
},
"013": {
"id": "013",
"label": "Bounded Sets, Maxima and Minima",
"meta": "",
"content": "The values inside a set of real numbers can be bounded.",
"notes": "013-snippet.html",
"video": "https://www.youtube.com/embed/",
"webwork": "",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto013?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"100": {
"id": "100",
"label": "Sequences",
"meta": " RA02 ",
"content": "These object are needed to define limits later on.",
"notes": "100-snippet.html",
"video": "https://www.youtube.com/embed/1SguKALJji8?start=17",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/UMN/calculusStewartCCC/s_11_1_5.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto100?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"101": {
"id": "101",
"label": "Convergence",
"meta": " RA02 ",
"content": "Convergent sequences have a well-defined limit.",
"notes": "101-snippet.html",
"video": "https://www.youtube.com/embed/1SguKALJji8?start=367",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.1_Sequences/10.1.31.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto101?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"102": {
"id": "102",
"label": "Boundedness",
"meta": " RA03 ",
"content": "Sequences can be bounded from above and from below.",
"notes": "102-snippet.html",
"video": "https://www.youtube.com/embed/k-Wm6gJYfrw?start=221",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/WinonaState/StewartCalcEarlyTran7ed/Chap11Section01/SCalcET7-11-1-037.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto102?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
"103": {
"id": "103",
"label": "Limit Theorems",
"meta": " RA04 ",
"content": "Combining limits is a useful tool.",
"notes": "103-snippet.html",
"video": "https://www.youtube.com/embed/237VMLNVtQs?start=18",
"webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Dartmouth/setStewartCh12S1/problem_7.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
"discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto103?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
"podcast": ""
},
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